---
title: "Time Series Homework: Chapter 3 Lesson 2"
subtitle: "Please_put_your_name_here"
format: 
  html:
    embed-resources: true
    toc: true
    code-fold: true
---

```{r, echo=FALSE, message=FALSE, warning=FALSE}

# Loading R packages
if (!require("pacman")) install.packages("pacman")
pacman::p_load(tidyverse, 
               tsibble, fable,
               feasts, tsibbledata,
               fable.prophet,
               patchwork,
               lubridate, 
               rio,
               ggplot2,
               kableExtra
               )
```

## Data

```{r, message=FALSE}

mortality <- rio::import("https://byuistats.github.io/timeseries/data/mortality_us.xlsx")

```

## Questions

### Question 1 - Context and Measurement (10 points)

The first part of any time series analysis is context. You cannot properly analyze data without knowing what the data is measuring. Without context, the most simple features of data can be obscure and inscrutable. This homework assignment will center around the series below.

Please research the time series. In the spaces below, give the data collection process, unit of analysis, and meaning of each observation for the series.

#### **US Mortality**

<https://wonder.cdc.gov/wonder/help/cmf.html#>

Note: The data is self-explanatory, don't get lost in the documentation page.

::: {.callout-note title="Answer" icon="false"}
<!-- Delete this and put your answer here. The three colons mark the end of your answer. -->
:::

### Question 2 - Key Definitions (10 points)

Answer the prompt to the learning outcome below. Include any mathematical expressions or illustrations that may accompany the definitions and ideas if available.

::: {.callout-note title="Answer" icon="false"}
-   **Explain forecasting by extrapolation**: <!-- Delete this and put your answer here. -->

-   **Define exponential weighted moving average (EWMA)** <!-- Delete this and put your answer here. -->

-   **Define the one-step-ahead prediction error (1PE)** <!-- Delete this and put your answer here. -->

-   **Indicate when the EWMA smoothing parameter is optimally set as 1/n** <!-- Delete this and put your answer here. -->
:::

### Question 3 - US Mortality Rate: Visualization (10 points)

##### a) Please plot the US Mortality Rate series.

::: {.callout-note title="Answer" icon="false"}
```{r}




```
:::

##### b) Please plot the decomposition of the US Mortality Rate series.

::: {.callout-note title="Answer" icon="false"}
```{r}



```
:::

### Question 4 - US Mortality Rate: Exponential Smoothing (25 points)

##### a) Use the exponential smoothing method to model the random component of the US Mortality Rate series. Use the smoothing parameter that R calculates by minimizing the SS1PE.

::: {.callout-note title="Answer" icon="false"}
```{r}



```
:::

##### b) Please repeat the modeling above but instead choose a smoothing parameter value $\alpha=0.2$

::: {.callout-note title="Answer" icon="false"}
```{r}
count(mortality_decom)
# Format as tsibble
mortality_ts <- mortality |>
  dplyr::select(year, `mort_rate_per_100,000`) |>
  as_tsibble(index = year)
mortality_decom <- mortality_ts |>
model(feasts::classical_decomposition(`mort_rate_per_100,000` ~ season(2), type = "mult")) |>
  components()

```
:::

##### c) Please repeat the modeling above but instead choose a smoothing parameter value $\alpha=\frac{1}{n}$

::: {.callout-note title="Answer" icon="false"}
```{r}



```
:::

##### d) Which of the smoothing parameter values you tried before work best fo the series? Justify your answer.

::: {.callout-note title="Answer" icon="false"}
<!-- Delete this and put your answer here. The three colons mark the end of your answer. -->
:::

### Question 5 - US Mortality Rate: Excess Mortality (45 points)

The jump at the last two years of the US Mortality Rate series is clearly the effect that Covid-19 had on mortality across the US.

##### a) Please calculate the excess mortality rate during 2020 and 2021 using the smoothing parameter values you employed in the previous question. Your results should be displayed in a table that is professionally formatted. Hint: We will need to apply the EWMA algorithm to the random component and later add the seasonal component and trend to our EWMA estimate.

::: {.callout-note title="Answer" icon="false"}
```{r}



```
:::

##### b) What is the meaning of excess mortality as you calculated it? Please explain it to a general audience, as if you were being interviewed in a national news show.

::: {.callout-note title="Answer" icon="false"}
<!-- Delete this and put your answer here. The three colons mark the end of your answer. -->
:::

##### c) Which excess mortality rate estimate do you think is correct? Some commentators would suggest you are choosing the parameters to defend your political goals, not to conduct a scientific analysis. Please comment on the difficulty of choosing parameter values to estimate the death toll of Covid-19.

::: {.callout-note title="Answer" icon="false"}
<!-- Delete this and put your answer here. The three colons mark the end of your answer. -->
:::

### Rubric

+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Criteria**                                                       | **Mastery (10)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 1: Context and Measurement**                       | The student thoroughly researches the data collection process, unit of analysis, and meaning of each observation for both the requested time series. Clear and comprehensive explanations are provided.                                                                                                                                                                                                                                                                                   | The student does not adequately research or provide information on the data collection process, unit of analysis, and meaning of each observation for the specified series.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (10)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 2: Definitions**                                   | The student provides sufficient evidence of mastery of the outcome prompt. The submission included mathematical expressions or illustration if available in the text or the Time Series Notebook                                                                                                                                                                                                                                                                                          | The student did not provide sufficient evidence to evaluate the outcome prompt.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (5)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 3a: Mortality Plot**                               | The student accurately plots the US Mortality Rate series in R, ensuring clear labeling and a descriptive title for easy interpretation. The visualization effectively presents the data with distinguishable points or lines and appropriate formatting. Additionally, the R code is well-commented, providing clear explanations of each step and maintaining readability.                                                                                                              | The student encounters challenges in plotting the US Mortality Rate series in R. The plot may lack essential labels or a descriptive title, making it difficult to interpret. Additionally, the visualization might be unclear or cluttered, and the R code may lack sufficient comments, hindering understanding of the process. Overall, improvement is needed in effectively plotting time series data in R.                                                                                                                                                                                                                                                          |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (5)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 3b: Decomposition plot**                           | The student plots the decomposition of the US Mortality Rate series in R, ensuring clear labeling and a descriptive title for easy interpretation of the decomposed components. The visualization effectively presents the trend, seasonal, and random components with distinguishable features and appropriate formatting. Additionally, the R code is well-commented, providing lucid explanations of each step in the decomposition process, ensuring readability and reproducibility. | The plot may lack essential labels or a descriptive title, making it difficult to interpret the decomposed components. Additionally, the visualization might be unclear or cluttered, and the R code may lack sufficient comments, hindering understanding of the process. Overall, improvement is needed in effectively plotting the decomposition of time series data in R.                                                                                                                                                                                                                                                                                            |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (5)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 4a: Smoothing SS1PE**                              | Students use R to compute exponential smoothing for modeling the random component of the US Mortality Rate series. Their R code is well-commented, providing clear explanations for each step of the process, ensuring transparency in the computational process.                                                                                                                                                                                                                         | Students may encounter challenges in implementing exponential smoothing in R, resulting in incomplete or ineffective computations. Their R code might lack sufficient comments, hindering clarity in understanding the computational process.                                                                                                                                                                                                                                                                                                                                                                                                                            |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (5)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 4b: Smoothing a=0.2**                              | Students employ R to repeat the modeling of the US Mortality Rate series using a specified smoothing parameter value of alpha=0.2. Their R code is well-commented, providing clear explanations for each step of the process, ensuring transparency in the computational process.                                                                                                                                                                                                         | Students may encounter challenges in implementing exponential smoothing in R, resulting in incomplete or ineffective computations. Their R code might lack sufficient comments, hindering clarity in understanding the computational process.                                                                                                                                                                                                                                                                                                                                                                                                                            |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (5)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                           | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 4c: Smoothing a=1/n**                              | Students employ R to repeat the modeling of the US Mortality Rate series using a specified smoothing parameter value of alpha=1/n. Their R code is well-commented, providing clear explanations for each step of the process, ensuring transparency in the computational process.                                                                                                                                                                                                         | Students may encounter challenges in implementing exponential smoothing in R, resulting in incomplete or ineffective computations. Their R code might lack sufficient comments, hindering clarity in understanding the computational process.                                                                                                                                                                                                                                                                                                                                                                                                                            |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (10)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 4d: Evaluation of Parameter Choice**               | Students justify their choice of parameter in the context of the underlying factors affecting US Mortality Rates evident in the data. The students evidence their understanding of the implications of the values in the smoothing parameter. Students show they have done some background research into the data to answer the question.                                                                                                                                                 | Students fail to adequately justify their choice of parameter in relation to the underlying factors affecting US Mortality Rates evident in the data. They may lack evidence of understanding the implications of the values in the smoothing parameter or fail to demonstrate how these implications relate to the context of the data. Additionally, they may show limited evidence of background research into the data to support their justification, indicating a lack of depth in their analysis.                                                                                                                                                                 |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (15)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 5a: Excess MortalityTable**                        | Students accurately calculate the excess mortality rate during 2020 and 2021 using the smoothing parameter values employed in the previous question. They present their results in table, clearly displaying the excess mortality rate for each year alongside the corresponding smoothing parameter values. The table is well-labeled and easy to interpret.                                                                                                                             | Students demonstrate inaccuracies in calculating the excess mortality rate during 2020 and 2021. Their presentation of the results in a table may lack clarity and professionalism, with issues such as unclear labeling, inconsistent formatting, or difficulty in interpreting the information provided. Additionally, they may overlook important details or fail to include all necessary information in the table, making it challenging for readers to understand the table.                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (10)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 5b: Excess Mortality**                             | Explanations effectively convey the meaning of excess mortality to a general audience, avoiding technical terms and providing a clear, accessible description. They define excess mortality as the number of deaths observed during a specific period compared to what would be expected based on historical data.                                                                                                                                                                        | Responses may struggle to explain excess mortality clearly to a general audience, potentially using technical language or lacking coherence. They may fail to provide relatable examples or context, making it difficult for the audience to understand the concept and its significance.                                                                                                                                                                                                                                                                                                                                                                                |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                    | **Mastery (20)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | **Incomplete (0)**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| #### **Question 5c: Evaluation of assumptions used for inference** | Responses address the challenge of selecting parameter values to make inference in time series. They provide a comprehensive analysis, considering factors like modeling assumptions, and methodological variations that influence parameter selection. Explanations highlight the need of transparent reporting to ensure robust and reliable estimates in professional discourse.                                                                                                       | Below expectations, responses may lack depth or clarity in addressing the challenge of selecting parameter values for making inference in time series. They may overlook key factors influencing parameter selection, such as data quality or specific characteristics of the time series data. Additionally, they may not effectively consider the impact of modeling assumptions or methodological variations on parameter selection. Furthermore, they may fail to emphasize the importance of transparent reporting in ensuring the reliability and validity of estimates, potentially resulting in a lack of confidence in the conclusions drawn from the analysis. |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| **Total Points**                                                   | **100**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
+--------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
